Mathematics, Computing and AI
The complexity of living systems necessitates novel mathematical theories, algorithms and machine learning.
The Mathematics, Computing, and AI PhD program at MPI-CBG is a home for mathematicians and computer scientists to create new mathematics - both pure and applied - to tackle the most challenging problems in science. We embrace the nonlinearities, high dimensionality, and multiscale structures that define many natural systems. Our research develops rigorous theory, innovative methodology, data analytics, and computational frameworks that shape new mathematical understanding across diverse domains.
Mathematics Across Scales and Dimensions
We span a rich spectrum of disciplines - algebra, topology, geometry, dynamical systems, combinatorics, scientific computing and visualization, network science, high-perofmrance computing and AI, united by a focus on multiscale patterns and multidimensional structure. We create new theoretical frameworks and algorithms capable of capturing both local and global organisation, from the fine geometry of spatial arrangements to the topology of complex networks.
High-dimensional and multiscale datasets enable us to draw on computational topology, metric geometry, multilinear algebra, and topological learning to extract invariants, reveal hidden symmetries, and quantify spatial and temporal organisation across scales. These same approaches also apply to abstract problems with no data, advancing mathematics in its own right while building bridges to applications in biology, physics, and the life sciences. We excel in sub-disciplines such as:
- Algebra
- Topology
- Geometry
- Dynamical Systems
- Combinatorics
- Scientific Computing & Visualization
- Network Science
- High-Performance Computing & AI
Large-scale datasets - microscopy images, genome sequences, and spatial molecular maps - often require sophisticated computational methods for analysis and interpretation, making computer science important in many contexts. In turn, complex scientific questions drive the creation of novel algorithms, simulations, and theoretical frameworks in computer science, with mathematics and computation together providing new perspectives on information processing in complex systems.
The program thrives on depth in theory, originality in methodology, and creativity in application. Projects often integrate novel mathematical concepts with high-performance computation, allowing us to explore phenomena where the underlying models, data, and scientific questions meet.
Our research is embedded in the collaborative environment of MPI-CBG, the Center for Systems Biology Dresden (CSBD), and the Max Planck Institute for the Physics of Complex Systems (MPI-PKS). This network brings together mathematicians, computer scientists, AI researchers, and experimental scientists, creating a vibrant intellectual ecosystem where new mathematics is conceived, developed, and applied to some of the most intricate problems in science.
Research Group Leaders Involved
The research group leaders (RGLs) principally involved include Türkü Özlüm Çelik · Daniela Egas Santander · Pierre Haas · Heather Harrington · Frank Jülicher · Aida Maraj · Carl Modes · Ivo Sbalzarini and Agnes Toth-Petroczy.
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